ABSTRACT
This chapter describes an approach for constructing invariant polynomials from link diagrams. It was proposed by Louis H. Kauffman. It is quite expressive and allows constructing polynomials. The first polynomial to be constructed coincides with the Jones polynomial up to a suitable variable change. So, one can also speak about the Jones– Kauffman polynomial or the Jones polynomial in Kauffman's form. The second polynomial includes some more sophisticated techniques in comparison with the first one. So, the second Kauffman polynomial is stronger than the first one. The chapter utilizes induction on the number of classical crossings. The induction basis is trivial.
